Description for the calculation of a rhombus
A rhombus is a quadrangular geometric shape and has the following characteristics
All four sides are the same length
The angles of the opposite corners are identical
The opposite sides are parallel to each other
\(a\) Length
\(h\) Height
\(A\) Area
\(P\) Perimeter
\(e\) Long diagonal
\(f\) Short diagonal
\( α\) Angle Alpha
\( β\) Angle Beta
\(A = a · h\)
\(\displaystyle A= \frac{e · f}{2}\)
\(A=a2 · sin(α)\)
\(a = A / h\)
\(\displaystyle a = \sqrt{\left(\frac{e}{2}\right)^2 + \left(\frac{f}{2}\right)^2}\)
\(\displaystyle h = \frac{A}{a}\)
\(h = sin(α) · a\)
\(b = sin(β) · a\)
\(P = 4 · a\)
\(\displaystyle P = 4 · \frac{h}{sin(α)}\)
\(\displaystyle P = 4 · \frac{h}{sin(β)}\)
\(\displaystyle e =\frac{ h }{ sin(α/2)}\)
\(\displaystyle e = a ·\frac{ sin(β)}{ sin(α/2)}\)
\(\displaystyle e = 2 · a · cos\left(\frac{α}{2}\right)\)
\(\displaystyle f =\frac{ h }{ sin(β/2)}\)
\(\displaystyle f = a ·\frac{ sin(α)}{ sin(β/2)}\)
\(\displaystyle f = 2 · a · cos\left(\frac{β}{2}\right)\)
\(\displaystyle β =\frac{asin( h) }{a}\)
Deutsch